A model is a simplified, abstracted representation of an object or system that presents only the information needed by its user. For example, the plastic models of aircraft I built as a kid abstract away everything except the external appearance, a mathematical model of a system shows only those dimensions and relationships useful to the model's users, a control system is a model of the relationships between the stimuli and the response desired by the designer and user of the larger system being controlled (evolution as designer and organism as user in biological analogy). A control system doesn't make a model of a system, to a large degree it is the designers' model of the system it controls.
At the simplest end are one-dimensional models, that we call measurements.
The most complex models are not explicit, they are too complex to be explicitly known, much less communicated; the model of the world that each person carries within his own mind.